[Sailfish]

I don't know if this will help much, but I'll throw it out there.

You mentioned the engine was installed 15 years ago. I owned a cobra with a very similar engine (342-s/n 105 with a 770 carb). I purchased the car new in 2007 and experienced all the same issues you're experiencing. I contacted the engine builder (Roush) and asked for help (the car was still under warranty). Roush was looking into it, and in the meantime, I made numerous modifications to the carb (new jets, new squirter, new cam, etc.). Ultimately, we were able to fix the vast majority of issues. Shortly after, Roush called and validated my carb was defective (a paint code on the carb verified it was part of a defective batch). Roush sent me a brand new 770 replacement carb, at no cost, and it worked like a champ. I put over 20,000 miles on the car and never made a carb adjustment.